Angular Regularity and Strichartz Estimates for the Wave Equation

Abstract

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular momentum operators. In this setting, the range of (q,r) exponents vastly improves over what is available for the wave equations based on translation invariant derivatives of the initial data and the dispersive inequality. Two proofs of this result are given.

34 pages. Updated with a simplified physical space proof by Igor Rodnianski

Cited by in corpus (12)

• Strichartz estimates on Schwarzschild black hole backgrounds
• The Strauss conjecture on Kerr black hole backgrounds
• Some Remarks on Strichartz Estimates for Homogeneous Wave Equation
• On the regularity set and angular integrability for the Navier--Stokes equation
• Strichartz estimates for wave equation with inverse square potential
• On almost global existence and local well-posedness for some 3-D quasi-linear wave equations
• Small data scattering for semi-relativistic equations with Hartree type nonlinearity
• The Glassey conjecture on asymptotically flat manifolds
• A Vector Field Method for Non-Trapping, Radiating Spacetimes
• Inhomogeneous Strichartz estimates with spherical symmetry and applications to the Dirac-Klein-Gordon system in two space dimensions
• Generalized Inhomogeneous Strichartz estimates
• Sharp Strichartz estimates in spherical coordinates